C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF CUNTZ-KRIEGER ALGEBRAS

Let CK* denote the C*-algebra defined as the direct sum of all Cuntz-Krieger algebras. We introduce a comultiplication Delta(phi) and a counit epsilon on CK* such that Delta(phi) is a nondegenerate *-homomorphism from CK* to CK* circle times CK* and epsilon is a *-homomorphism from CK* to C. From this, CK* is a counital non-commutative non-cocommutative C*-bialgebra. Furthermore, tensor products of representations and C*-subbialgebras of CK* are investigated.